$($a$)$

Find

lim$$x$0$

$1$ cos$($x$)$x$2$

$.$

$($b$)$

Use your answer to part $($a$)$ to derive the approximation

cos$($x$)1$

$12$

x$2$

for x near $0.$

For

x $0.$

$1$ cos$($x$)$x$2$

$$

$1$ cos$($x$)$

cos$($x$)1$

$($c$)$

Use your answer to part $($b$)$ to approximate

cos$(0\mathrm{.}06).$

$($d$)$

Use a calculator to approximate

cos$(0\mathrm{.}06)$

to four decimal places.

Compare the result with part $($c$).$

The result from part $($c$)$ is the same to four decimal places.The result from part $($c$)$ is not the same to four decimal places.$$